Simplify the following expression: $z = \dfrac{y^2 + 13y + 42}{y + 6} $
First factor the polynomial in the numerator. $ y^2 + 13y + 42 = (y + 6)(y + 7) $ So we can rewrite the expression as: $z = \dfrac{(y + 6)(y + 7)}{y + 6} $ We can divide the numerator and denominator by $(y + 6)$ on condition that $y \neq -6$ Therefore $z = y + 7; y \neq -6$